Problems on Simultaneous Equations
Solve the following Systems of linear equations : 1. If one number is thrice the other and their sum is 60, find the numbers. 2. Find the fraction which becomes 1/2 when the denominator is increased by 5 and is equal to 1/3 when the numerator is diminished by 4..
Relation between the roots of a quadratic equation
Our investigation reveals that there is a definite relationship between the roots of a quadratic equation and the coefficient of the second term and the constant term. The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term divi..
Operation on Real Functions
The following are the Operation on Real Functions: Sum Function, Difference Function, Product Function, Quotient Function, Scalar Multiplication Function, Composite Functions, Inverse Function..
Factorising Trinomials
When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try to express a trinomia..
When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try to express a trinomia..Factorization Summary
Summary - If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If the polynomial can be expressed as the difference of two squares, we use a 2 - b..
Summary - If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If the polynomial can be expressed as the difference of two squares, we use a 2 - b..Second Method:
x 2 + 8x + 15 = x 2 + 5x + 3x + 15 (after noticing that 5 + 3 = 8 and 5 3 = 15) = x(x +5) + 3(x + 5) = (x + 5) (x + 3) Resolve into factors: x 2 - 15x + 56 x 2 - 15x + 56 Take factors of 56 having their sum = -15 They are -8, -7. \ x 2 - 15x + 56 = x 2 - 7x - 8x + 56 \ x ..
x 2 + 8x + 15 = x 2 + 5x + 3x + 15 (after noticing that 5 + 3 = 8 and 5 3 = 15) = x(x +5) + 3(x + 5) = (x + 5) (x + 3) Resolve into factors: x 2 - 15x + 56 x 2 - 15x + 56 Take factors of 56 having their sum = -15 They are -8, -7. \ x 2 - 15x + 56 = x 2 - 7x - 8x + 56 \ x ..Quadratic Equations Roots and Conditions
Formation of quadratic equations from given roots and conditions - Formation of quadratic equations from given roots and conditions. i) The quadratic equations whose roots are a and b is where S = sum of roots and P = product of roots ii) Quadratic equations with real coefficients, the co..
Formation of quadratic equations from given roots and conditions - Formation of quadratic equations from given roots and conditions. i) The quadratic equations whose roots are a and b is where S = sum of roots and P = product of roots ii) Quadratic equations with real coefficients, the co..Worked Examples on Simultaneous Equations
Problems on Simultaneous Equations - If one number is thrice the other and their sum is 60, find the numbers. Let the numbers be x and y. x is 3 times y x = 3y (1) Sum of x and y is 60 x + y = 60 (2) Putting the value of x from (1) in (2), we get, 3y + y = 60 4y = 60 y = 15 Subs..
Problems on Simultaneous Equations - If one number is thrice the other and their sum is 60, find the numbers. Let the numbers be x and y. x is 3 times y x = 3y (1) Sum of x and y is 60 x + y = 60 (2) Putting the value of x from (1) in (2), we get, 3y + y = 60 4y = 60 y = 15 Subs..Formula
Number of sides of a polygon = n the required formula is = d = n -3 The sum of the reciprocal of x and the reciprocal of y equals the reciprocal of m. Express this as a formula. Reciprocal of Reciprocal of Reciprocal of The required formula is ..
Number of sides of a polygon = n the required formula is = d = n -3 The sum of the reciprocal of x and the reciprocal of y equals the reciprocal of m. Express this as a formula. Reciprocal of Reciprocal of Reciprocal of The required formula is ..Choose an algebraic expression for " The sum of three consecutive even..
Choose an algebraic expression for " The sum of three consecutive even integers, if u is the first even integer". => u + ( u + 2) + ( u + 3) or u + ( u + 1) + ( u +2) or u + 2 + 4 or u + ( u + 2) + ( u + 4)..
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